Capability analysis measures the ability of a process to meet specifications when the process is in statistical control.
A process must be in control before attempting to assess the capability. An out-of-control process is unpredictable and not capable of been characterized by a probability distribution.
Most process capability indices assume a normally distributed quality characteristic. If the distribution is non-normal, it may be possible to transform the data to be normally distributed. The process mean and process sigma define the normal distribution.
If the process is stable over time, the estimates of short-term sigma and long-term sigma are very similar. They are both estimates of the same parameter, although statistically speaking the long-term sigma is a slightly more efficient estimator.
However, if there are any changes in the process mean over time, the estimate of long-term sigma is greater than that of short-term sigma. The larger the difference between the values of long-term and short-term indices, the more opportunity there is to improve the process by eliminating drift, shifts and other sources of variation.
